Calculating the Value of a 7-Year Ordinary Annuity

B

The value of the annuity = (200/0.05)*(1- 1/(1.05^7)) = 1,157

To calculate the present value of an ordinary annuity, you can use the formula:

PV = PMT × [(1 - (1 + r)^(-n)) / r],

where PV is the present value, PMT is the payment per period, r is the required rate of return per period, and n is the number of periods.

In this case, the investor wants to calculate the present value of a seven-year ordinary annuity that pays $200 per year, with a required rate of return of 5% per year.

Using the given values, we have: PMT = $200, r = 5% or 0.05 (as a decimal), n = 7.

Substituting these values into the formula, we can calculate the present value:

PV = $200 × [(1 - (1 + 0.05)^(-7)) / 0.05]

Calculating the expression within the brackets first: (1 + 0.05)^(-7) ≈ 0.722 (1 - 0.722) ≈ 0.278

Now, substitute the calculated value into the formula: PV = $200 × (0.278 / 0.05)

PV ≈ $1,115.60

Therefore, the investor should pay approximately $1,115.60 for the seven-year ordinary annuity.

None of the given answer choices match the calculated value exactly. The closest option is option D, which is $1,213. It's possible that there may be a rounding error or a mistake in the answer choices provided.